Problem 6 worked answer
The Stained-Glass Window
Designed for Grade 3 · Uses Middle Grade 3 math · About 2–6 minutes
At a glance
- Part 1: The window is initially purple.
- Part 2: Alex must change 3 clear panes to purple. The new purple fraction is , which is equivalent to .
1. Name the starting fraction
The denominator counts all equal panes in the whole window. There are 8 equal panes, so the denominator is 8. The numerator counts the purple panes. There are 3 purple panes, so the numerator is 3.
The starting purple fraction is .
2. Make the numerator two less than the denominator
The denominator stays 8 because Alex does not add or remove any panes. A numerator exactly 2 less than 8 must be
.
Alex needs 6 purple panes altogether. She already has 3, so she must change
clear panes to purple.
The finished window is purple. Writing is mathematically equivalent, but directly shows 6 of the original 8 panes.
Check
After the change, . Two clear panes remain, and , so the numerator 6 is exactly 2 less than the denominator 8.
Technical fit and rating
Number and operations
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